Question

If $f\left(x\right)=\sin x,g\left(x\right)=1+x^3$, then $\left(fog\right)\left(x\right)$ equals

• A. ${\sin }^{3}x$
• B. $\cos (1+x^3)$
• C. $\sin (1+x^3)$
• D. ${\cos }^{3}x$

Answer 1

Answer: (C)

$\sin (1+x^3)$

Given that, $f\left(x\right)=\sin x,g\left(x\right)=1+x^3$

$\left(fog\right)\left(x\right)=f\left(g\left(x\right)\right)$

$=f(1+x^3)=\sin (1+x^3)$